Let's analyze the given function:
[tex]\[ h(x) = 0.000371(x^2 - 1280x) + 152 \][/tex]
This function represents the height [tex]\( h \)[/tex] of the cable above the ground as it relates to [tex]\( x \)[/tex], the horizontal distance from the left tower. To find the height of the towers, we need to determine the height at the point where [tex]\( x = 0 \)[/tex].
Step-by-Step Solution:
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ h(0) = 0.000371(0^2 - 1280 \times 0) + 152 \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ h(0) = 0.000371(0 - 0) + 152 \][/tex]
[tex]\[ h(0) = 0.000371 \times 0 + 152 \][/tex]
3. Since [tex]\( 0.000371 \times 0 = 0 \)[/tex], the equation simplifies to:
[tex]\[ h(0) = 0 + 152 \][/tex]
[tex]\[ h(0) = 152 \][/tex]
Therefore, the height of the towers is [tex]\( 152 \)[/tex] meters.
So the correct answer is:
(B) 152
